Musical instrument tuning apparatus



April 11, 1939. L, B, HOLMES MUSICAL INSTRUMENT TUNING APPARATUS Filed Aug. 10, 1936 2 Sheets-Sheet 1 4,65 zer5.ho;me5,

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A ril 11, 1939. L. B. HOLMES 2,153,800

MUSICAL INSTRUMENT TUNING APPARATUS Filed Aug. 10, 1936 2 Sheets-Sheet 2 uzok. 554355. mPZjGwo KO: ZOE

Patented Apr. 11, 1939 UNITED STATES PATENT OFFICE 12 Claims.

This invention relates to apparatus for tuning musical instruments or for observing and analyzing sound waves. More particularly, this invention relates to visual observation apparatus adapted to generate certain predetermined standard frequencies having certain predetermined intervals therebetween for tuning musical instruments or determining when certain sound frequencies are of a predetermined pitch or pitches.

An object of this invention is to provide an oscillation generator having means for generating a series of predetermined frequencies and a cathode ray device adapted to have one of said predetermined standard frequencies impressed thereon simultaneously as a sound modulated electric current is impressed thereon whereby the frequency characteristics of. the standard frequency and the sound may be observed on the screenof the cathode ray device.

Another object of this invention is to provide a device for determining sound frequencies, said device having an oscillation generator adapted to generate any one of a selected number of frequencies and an electrically energized visual observation device adapted to receive electrical oscillations from said oscillation generator corresponding to said selected frequency and electrical sound modulated oscillations corresponding to the frequency of the sound being measured whereby frequency differences that may exist between the oscillation generator frequency and the sound frequency may be rendered visible.

A further object of this invention is to provide a standard frequency device and an indieating device having means for impressing a selected standard frequency on the circuits thereof together with a sound modulated electric current for producing a visual indication of any fre quency differences that may exist between the 40 standard frequency and the sound frequency.

Other and further objects of this invention will be apparent to those skilled in the art to which it relates from the following specification and the claims.

In accordance with this invention I provide a visual indicating apparatus employing av device, such as a cathode ray tube, having means for generating a cathode ray and deflecting electrodes for moving the cathode ray beam over a screen in accordance with electrical potentials of a predetermined frequency and a sound frequency impressed on said electrodes. A standard frequency oscillator employing a series of twelve tuning forks, for example, having frequencies spaced at predetermined intervals, such as are employed in an octave of a piano scale, for instance, from each other, is connected to electrodes of. the visual cathode ray devicetogether with the output of the sound pick-up amplifier in such a manner that the cathode ray is caused to produce predetermined flgures on the screen of the cathode ray device when the sound frequency bears a certain relationship or relationships to the standard frequency being produced by the standard frequency oscillator.

By selecting any one of the predetermined number of tuning forks and causing the standard frequency oscillator to produce oscillations of a frequency corresponding to the tuning fork, the frequencies of different sounds, produced by a musical instrument, for example, may be measured, matched, or observed on the screen of the cathode ray device.

The apparatus of this invention is very simple in use and enables a person to tune a musical instrument to a predetermined standard frequency by sight. The apparatus also may be employed in the instruction of music and in demonstrating principles of sound physics.

Further details of this invention will be apparentfrom the following specification and the drawings in which, briefly,

Figure 1 shows a schematic diagram of the circuit arrangement employed;

Figures 2 and 3 are detailed views showing the mounting of the tuning forks and associated apparatus;

Figures 4, 5, 6, and '7 show different frequency patterns that may be obtained on the cathode ray tube screen, and Figure 8 shows the control panel of an apparatus constructed in accordance with this invention.

Referring to Figure 1 of the drawings in detail. reference numeral I designates a cathode ray tube having deflecting plates 2 and 3, anodes 4 and 5, grid electrode 6, cathode I, and heater electrode 8. Y

A source of direct current supply is connected to the terminals l2 and i3. This source may be a generator, battery, or a rectified and filtered alternating current supply, such as the supply M. A condenser I5 is connected across the terminals l2 and 13 together with a voltameter I6 and a series of resistance units 9, I0, and II. These resistance units are employed as voltage dividers for the purpose of impressing predetermined or variable voltages on selected electrodes of the tube I as is hereinafter described. The connection I! between the resistors 9 and I0 is employed to connect the cathode l to the direct current source of supply. A variable contact and connection l8 provided to the resistor 9 is used to impress a negative voltage on the grid electrode 6 of the tube with respect to the oathode I. A similar variable connection I9 is provided to the resistor ID for impressing a positive potential on the anode 5 with respect to the cathode One of each of the sets of deflector plates 2 and 3 is connected to the anode 4 which is connected to the positive terminal l3 and to the resistor'll.

The microphone is connected across the resistor 2| to the grid electrode of the amplifier tube 22 and the grid bias resistor 23. A bypass condenser 24 is connected across the resistor 23 which is crnnected into the cathode circuit of the tube 22. The anode of the tube 22 is connected to the primary of the coupling transformer 25, the secondary of which is connected to the control grid of the amplifier tube 26. A grid bias resistor 21 and bypass condenser 28, similar to those of the tube 22 are connected into the cathode circuit of the tube 26. The anode of the tube 26 is connected to the primary of the transformer 21 and the secondary of this ,transformer is connected across the resistor 28 associated with the cathode ray tube The resistor 28 is connected in series with the resistor 29 between one deflector plate of each set of deflector plates 2 and 3. The connection between the resistors 28 and 29 is also joined to the anode 4 of the tube The tuning fork oscillator 30 comprises an oscillator tube 3| having cathode, anode, and grid electrodes, a pair of transformers 32 and 33, a tuning fork 34 and tuning fork transformers 35 and 36. The transformer 32 is connected between the grid and cathode electrodes of the tube 3| and the tuning transformer 35. The transformer 33 is connected between the cathode and anode electrodes of the tube 3| and the tuning fork transformer 36. The secondary of the transformer 33 is also connected to the primary of the transformer 31 and the secondary of this latter transformer is connected across the potentiometer 38.

Two electric discharge devices 39 and 40 are employed in accordance with this invention to produce electrical oscillations of a sawtooth wave form. The electric discharge device 39 is of the pentode type and is employed as a substantially constant current conducting device for periodically charging the condenser 4| after this condenser is periodically discharged through the gaseous three-electrode discharge device 40. The grid electrode of the discharge device 40 is connected to the variable contact 42 of the potentiometer 38 and the operation of this discharge device is accordingly controlled by the tuning fork oscillator 30 to discharge this condenser at a frequency determined by the frequency of the tuning fork oscillator. A resistor 43 is connected in series with the grid of the discharge device 44 as a current limiting device. A terminal of the secondary of the transformer 31 is connected to one of the grid electrodes of the pentode 39 and to the voltage divider 44 which is connected across the output terminals of the current supply H. The cathode and the auxiliary grid electrode of the discharge device 39 are connected through the resistor 45 to the control grid of this discharge device and to the negative terminal of the current supply source I4. This resistor 45 is employed to maintain the cathode and the control grid of the discharge device 39 at proper biasing potentials with respect to each other. The anode of the discharge device 40 is connected to the positive terminal of the current supply source I4 through the resistor 43 which is also employed as a current limiting device. The condenser 4| is connected to the cathode of the discharge device 40 and to the anode of this discharge device through the resistor 48. This condenser may be made variable so that the time interval of its charge through the constant current tube 39 may be controlled by varying its capacity. Another way of varying this time interval is by increasing or decreasing the current flow through the tube 39. A coupling condenser 41 is provided between the cathode of the discharge device 40 and the resistor 29 which is connected to one of the deflector plates 2 of the cathode ray tube I. The resistor 48 is connected across the output of the sawtooth oscillation generator, one terminal of this resistor being connected to the condenser 4| and the other terminal being connected to the condenser 41. This resistor may be made of a value such as to discharge the condenser 4| periodically to operate the saw tooth oscillator at some determinable frequency so that the tuning fork oscillator will have to function only as a master oscillator for controlling the saw tooth oscillator frequency. The output of the saw tooth oscillation generator is connected across the resistor 29 and across the deflector plates 2 of the cathode ray tube to swing the beam of the cathode ray tube horizontally at a frequency corresponding to the frequency generated by the tuning fork oscillator. The wave form of this saw tooth oscillator resembles the teeth of a saw in that it rises gradually in value up to a maximum and then practically instantly drops to minimum.

The source of current supply |4 includa a transformer 49 which is provided with a primary 50 adapted to be connected to a -volt alternating current lighting circuit, if desired. Filament heating secondary windings SI, 52, and 53 for heating the filaments of the discharge devices 39, 54, and 40, respectively, are also provided to the transformer 49. A relatively high voltage secondary 55 connected to the anode electrodes of the rectifier discharge device 54 and to the filter condensers 56, is also wound on the core of the transformer 49. The output of this secondary winding 55 is rectified by the rectifier discharge device 34 and filtered by the filter circuit comprising the condensers I3 and the resistance or choke coils 51. The output of this filter circuit is connected to the positive and negative terminals of the power supply.

The anode circuits of the amplifier tubes 22 and 26 also may be energized from the power supply source l4 or if desired, separate sources of current supply may be employed for these amplifier tubes. A separate source of current supply 3|a has been shown for the tuning fork oscillator tube 3|. However, it is apparent that this oscillator tube also may be energized from the power supply source H. The positive terminal of the power supply source I4 is connected to the metal chassis or cabinet of the cathode ray tube, the cathodes of the amplifier tubes, and the tuning fork oscillator tube cannot be connected to the cabinets but must be electrically isolated therefrom if the same source of anode current supply is to be used for the tuning fork oscillator and the amplifier tube as is used for the cathode ray tube. It is desirable to shield the different units, such as, the tuning fork oscilauaaoo lator, the amplifler and cathode ray tube circuits from each other to prevent undesired electrical coupling.

In Figure 2 I have shown the'preferred method of mounting the 12 tuning forks. employed'in the tuning fork oscillator, upon a rotatable carrier 66. Figure 3 illustrates the manner in which the tuning fork 34 is supported between the windings of the transformers l6 and 36. Suitable brackets 35a and 360 which clamp the windings I6 and 36, respectively, and support these windings on a panel 36b are provided to the transformers 36 and 36, respectively. These brackets function to support the transformers 86 and 36 rigidly with respect to the forks of the tuning fork positioned therebetween. The end of each of the tuning forks is provided with a suitable nut, such as, the nut Nb, to fasten the respective forks to the rotatable carrier member 60 which, is preferably of relatively massive construction in order to reduce vibration thereof when the tuning forks supported thereby are set into vibration. I employ a hammer having a head 62 made of relatively soft rubber, felt, leather, or similar material supported by the elongated spring-like member 63 in such a manner that the head 62 will strike succeeding ones of the tuning forks as the carrier member 60 is rotated by the shaft 64' in the direction designated by the arrow. The carrier member 60 is fastened to the shaft 66 by the set screw 66. The shaft 66 extends through a suitable hole in the panel 66 and has attached to the end thereof a suitable knob 61, shown in Fig. 8, which is employed for rotating the carrier member 60. The front of this panel 66 is provided witha series of twelve legends extending around a circle, the center of which coincides with the center of the knob 61. These legends correspond to the chromatic scale of a piano and are designated as c, c#, d, d#, e, e#, f, f#, g, g#, a, a#, b. These are the tones produced by the tuning forks supported by the rotatable carrier member 60 as designated in Figure 2.

As the knob 61 is rotated, different ones of the tuning forks supported by the carrier 61, corresponding to the different tones of the chromatic scale, are brought into position between the tuning fork transformer windings 35 and 36. Simultaneously, the pointer 68 of the knob 61 indicates on the front of the panel 66 which tuning fork is in position between the tuning fork transformer windings. As the different tuning forks are brought into position between the transformer windings, they are given a light tap by the head 62 of the hammer. Thus the tuning fork brought into position is set into vibration and through a feed-back action between the output and input circuits of the electric discharge device 3i the tuning fork is maintained in vibration as long as the electric discharge device 3| is energized.

The operation of this apparatus is as follows. In tuning a given note, for example, that corresponding to A of a piano to a standard pitch of 440 cycles per second, to determine if the string corresponding to this note is in tune, the operator rotates the knob 61 until the pointer 66 is opposite the position marked A. This rotates the tuning fork corresponding to A into position between the tuning fork transformers 35 and 36. The tuning fork is set into vibration when it is moved into this position inasmuch as it is tapped lightly by the hammer 62 and the tuning fork oscillator iscaused to generate electrical oscillations corresponding to 440 cycles per second. The output of the tuning fork oscillator is fed to the saw tooth oscillator which produces a pulsating current corresponding to the frequency of the tuning fork oscillator but having a different wave form suitable for controlling the sweep circuit of the cathode ray tube. The deflector electrodes 2 of the cathode ray tube are included in the sweep circuit of this tube and control the horizontal movement of the cathode ray beam, that is, the

electrical potential impressed upon these electrodes causes the cathode ray beam to sweep horizontally across the screen of the tube. For this reason electrical potentials having saw tooth wave form must be applied to these deflector electrodes inasmuch as the cathode ray beam must be swept across the tube screen in a predetermined time interval and then practically instantaneously returned to its original or starting position to repeat the sweeping cycle. This will be more clearly explained in connection with the explanation of Figures 4, 5, 6, and 7.

The sound from the musical instrument being tuned is picked up by the microphone 20 and translated into corresponding electrical vibrations which are amplified by the amplifier tubes 22 and 26 and associated circuits. The output of the amplifier is impressed on the deflector electrodes 3 of the cathoderay tube. These deflector electrodes are positioned substantially at right angles-to the deflector electrodes 2 as is customary 'in cathode ray tube design, and control the movement of the cathode ray beam in the vertical direction. Thus when the frequency of the sound picked up by the microphone 20 is the same as the frequency of the tuning fork oscillator, the figure observed on the cathode ray tube screen will be substantially like that illustrated in Figure 4. The instantaneous values of the sound wave intercepted by the microphone 20 over a complete cycle of the sound wave are exhibited on the screen of the cathode ray tube and a pattern similar to that shown in Figure 4 is obtained inasmuch as the time interval of one cycle of the sound wave intercepted by the microphone 20 corresponds to one cycle of the tuning fork oscillator. When this is the case, the figure exhibited on the cathode ray tube screen appears to be stationary. When the string of the musical instrument under observation is one-half the frequency of the tuning fork oscillator frequency, the pattern exhibited on the cathode ray tube screen is substantially like that illustrated in Figure 5. The pattern illustrated in Figure 4 will be present dimly in the background in the pattern illustrated in Figure 5, inasmuch as this pattern corresponds to the second harmonic. When the frequency of the string under observation is twice the frequency of the tuning fork oscillator, the pattern exhibited on the cathode ray tube screen will be that corresponding to Figure 6. Likewise, when the frequency of the string under observation is three times that of the standard frequency, the pattern will correspond to that shown in Figure 7.

I have illustrated the deflector plates 2 and 3 of the cathode ray tube in Figures 4, 5, 6, and 7 on the outside of the tube screen to show the relative positions of these deflector plates in order to facilitate explanation of this. invention.

modifications in the apparatus of my invention may be made, as will be apparent to those skilled in the art to which it relates. For example, different forms of electromechanically vibratile vibrator elements'may be employed instead of the tuning fork controlled oscillator. It is therefore to be understood that I do not desire to limit this invention to the exact details set forth except insofar as those details may be defined by the claims.

What I claim and desire to secure by Letters Patent is as follows:

1. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having an electromagnetic device and a plurality of tuning forks of different predetermined standard frequencies, movable supporting means for said tuning forks for moving selected ones 'bf said forks into predetermined relationship with the magnetic circuit of said electromagnetic device and means for setting the selected fork into vibration as said fork is moved into said predetermined relationship, a pick-up device for producing pulsating electric currents of certain sound frequencies of a musical instrument the frequency characteristics of which are to be determined, a cathode ray tube having a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of a plurality of said standard frequencies on selected electrodes of said cathode ray tube for sweeping said beam across said screen and means for amplifying and impressing electric currents corresponding to said pulsating electric currents upon other electrodes of said cathode ray tube for depflecting said cathode ray beam in accordance with said sound frequencies as said beam is swept across said screen whereby the frequency characteristics and sound quality of said instrument may be observed.

2. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having an electromagnetic device and a plurality of tuning forks of different predetermined standard frequencies, movable supporting means for said tuning forks for moving selected ones of said forks into predetermined relationship with the magnetic circuit of said electromagnetic device and means for setting the selected fork into vibration as said fork is moved into said predetermined relationship to generate electrical oscillations having a frequency corresponding to that of the selected fork, a cathode ray tube having a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of a plurality of said standard frequencies on selected electrodes of said cathode ray tube for sweeping said beam across said screen, a sound pick-up device for receiving sounds of the musical instrument being observed and means for amplifying and impressing electrical oscillations corresponding in frequency to said sounds upon other electrodes of said cathode ray tube for deflecting said cathode ray beam in accordance with said sound frequencies as said beam is swept across said screen whereby the frequency characteristics and sound quality of said instrument may be observed.

3. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having an electromagnetic device and a plurality of tuning forks of different predetermined frequency characteristics, movable supporting means for said tuning forks for moving selected ones of said forks into predetermined relationship with the magnetic circuit of said electromagnetic device and means for setting the selected fork into vibration as said fork is moved into said predetermined relationship, a cathode ray tube having a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for producing electrical oscillations of saw-tooth wave form corresponding in frequency to any one of a plurality of said standard frequencies and means for impressing said saw tooth oscillations on selected electrodes of said cathode ray tube for sweeping said beam across said screen, a sound pick-up device for receiving sounds of the musical instrument being observed and means for amplifying and impressing electrical oscillations corresponding in frequency to said sounds upon other electrodes of said cathode ray tube for deflecting said cathode ray beam in accordance with said sound frequencies as said beam is swept across said screen whereby the frequency characteristics and sound quality of said instrument may be observed.

4. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having an electromagnetic device and a plurality of tuning forks of different predetermined frequency characteristics, movable supporting means for said tuning forks for moving selected ones of said forks into predetermined relationship with the magnetic circuit of said electromagnetic device and means for setting the selected fork into vibration as said fork is moved into said predetermined relationship, a pick-up device for producing pulsating electric currents of certain sound frequencies the frequency characteristics of which are to be determined, an indicating device for producing a visible pattern re sulting from the combined effects of the selected standard frequency and the sound frequency being measured.

5. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having an electromagnetic device and a plurality of tuning forks of different predetermined frequency characteristics, a rotatable disc-like supporting means for said tuning forks, said supporting means having holes formed around the circumference thereof for receiving the bases of said tuning forks, means for rotating said supporting means for moving selected ones of said forks into predetermined relationship with the magnetic circuit of said electromagnetic device and means for setting the selected fork into vibration as said fork is moved into said predetermined relationship, a pick-up device for producing pulsating electric currents of certain sound frequencies the frequency characteristics of which are to be determined, an indicating device for producing a visible pattern resulting from the combined effects of the selected standard frequency and the sound frequency being measured.

6. In apparatus for observing characteristics of sounds of musical instruments and the like, the combination of an oscillation generator including a plurality of electromechanically vibratile vibrators of standard predetermined frequencies corresponding to the frequencies of an octave of a musical scale, movable supporting means for said vibrators for moving selected ones of said vibrators into operative position in said generator and means for setting the selected vibrator into vibration as it is selected, a cathode ray tube having a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of a plurality of said standard frequencies on selected electrodesof said cathode ray tube for observed.

7. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having a plurality of standard frequency vibrators of diiferent predetermined frequencies, means for selecting different ones of said vibrators and setting the selected vibrator into vibration for causing said oscillation generator to generate electrical oscillations having a frequency corresponding to that of the selected vibrator, a cathode ray tube having a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of a plurality of said standard frequencies on selected electrodes of said cathode ray tube for sweeping said beam across said screen, a sound pick-up device for receiving sounds of the musical instrument being observed and means for amplifying and impressing electrical oscillations corresponding in frequency to said sounds upon other electrodes of said cathode ray tube for modulating said cathode ray beam in accordance with said sound frequencies as said beam is swept across said screen whereby the sound quality of and wave form of the sounds received from said instrument may be observed on said screen.

8. In apparatus for tuning musical instruments the combination of a standard frequency oscillation generator having an electromagnetic device and a plurality of tuning forks of different predetermined frequency characteristics, said electromagnetic device having a magnetic circuit adapted to include selected ones of said tuning forks, means for setting the selected fork into vibration when said fork is included in the magnetic circuit of said electromagnetic device, a cathode ray tube having a screen, means for generating a beam of .cathode rays and a plurality of electrodes for controlling said beam, means for producing electrical oscillations of saw-tooth wave form corresponding in frequency to any one of a plurality of said standard frequencies and means for impressing said saw tooth oscillations on selected electrodes of said cathode ray tube for sweeping said beam across said screen, a sound pick-up device for receiving sounds of the musical instrument being observed and means for amplifying and impressing electrical oscillations corresponding in frequency to said sounds upon ating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of said plurality of standard frequencies corresponding to said musical tones on selected electrodes of said cathode ray tube for sweeping said beam across said screen at a rate determined by the selected musical tone, a sound pick-up device for receiving sounds corresponding substantially to the aforesaid musical tone selected or to harmonics thereof, of the musical instrument being observed and means for impressing electrical oscillations corresponding in frequency to said sounds upon other electrodes of said cathode ray tube for modulating said cathode ray beam in accordance with said sound frequencies as said beam is swept across said screen whereby the sound quality of and the wave form of the sounds received from said instrument may be observed on said screen.

10. In apparatus for observing characteristics of sounds of musical instruments and the like, the combination of an oscillation generator including means for producing a plurality of standard predetermined frequencies corresponding to the frequencies of an octave of a musical scale, a cathode ray tube having'a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of said standard frequencies on selected electrodes of said cathode ray tube for sweeping said beam across said screen at a rate determined by the selected standard frequency, a pick-up device for producing electrical oscillations corresponding to sound frequencies of the musical instrument being observed and means for impressing said electrical oscillations upon other electrodes of said cathode ray tube for deflecting said cathode ray beam substantially at right angles to the direction of the aforesaid sweeping, in accordance with said sound frequencies as said beam is swept across said screen whereby the frequency characteristics and sound quality of said instrument may be observed on said screen.

11. In apparatus for observing characteristics of sounds of musical instruments and the like, the combination of an oscillation generator including a plurality of vibrators of standard predetermined frequencies having a predetermined relation to each other in a musical scale, means for selecting one of said vibrators and means for generating electrical oscillations in accordance with the vibrations thereof, a cathode ray tube having a screen, means for generating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for impressing any one of a plurality of said standard frequencies on selected electrodes of said cathode ray tube for sweeping said beam across said screen periodically in accordance with the selected frequency in the musical scale, a pick-up device for producing electrical oscillations corresponding in -wave-form substantially to selected tones of the musical instrument being observed and means for impressing said electrical oscillations upon other electrodes of said cathode ray tube for deflecting said cathode ray beam in a direction substantially at right angles to said sweeping direction, in accordance with said tonal frequencies as said beam is swept across said screen whereby the frequency characteristics and sound quality of said instrument may be observed on said screen.

12 In apparatus for observing characteristics of sounds of musical instruments and the like, the combination of an oscillation generator in-- eluding a plurality of electromechanically vibratile vibrators of standard predetermined frequencies corresponding to the frequencies of an octave of a musical scale, a cathode ray tube havin: a screen. meanssforgenerating a beam of cathode rays and a plurality of electrodes for controlling said beam, means for producing electrical oscillations of saw-tooth wave form correspending in frequency to any one of a plurality of said standard frequencies and means for impressing said saw-tooth oscillations on selected electrodes of said cathode ray tube for sweeping said beam across said screen periodically in accordance with the selected frequency in the musical served on said screen.

IBB'I'ER B. HOLMES. 

